SSS 01

Sigma Series in Stochastics, Volume 1, 117131 Heldermann Verlag 2004 White Noise Theory and Physics Takeyuki Hida Meijo University, Nagoya, Japan White noise theory has extensively developed since it was started about a quarter of a century ago. The theory has been originated by physics, particularly by quantum dynamics, while mathematically it is mainly based on classical functional analysis. After its establishment, white noise analysis soon exhibited a major impact on the mathematical approach to quantum mechanics. Two ideas born at the beginning of the last century can be identified in the history of science paving the way for the development of white noise theory. In physics quantum mechanics opened a new "stochastic" chapter in exact sciences. In mathematics the proposal of Lebesgue integral made it possible to extend probability theory to cover almost any branch of science. Looking at these historical developments, the beauty of science on the one hand and the change of paradigm caused by stochastics on the other hand become visible. 